Begin by bringing a large pot of salted water to a boil. Add the spaghetti and cook until al dente, according to the package instructions.
Meanwhile, in a large bowl, combine the lemon zest, lemon juice, and olive oil. Stir in the grated Parmigiano Reggiano cheese to create a paste.
Once the spaghetti is cooked, reserve a cup of the pasta water, then drain the pasta.
Add the hot spaghetti to the lemon and cheese mixture, tossing well to combine. Gradually add the pasta water, a bit at a time, continuing to toss until a creamy sauce forms. The heat of the pasta will melt the cheese and emulsify the sauce.
Season with salt and a generous amount of black pepper. Stir in the torn basil leaves.
Serve immediately, garnishing with additional Parmigiano Reggiano cheese, if desired.
